Math 615 Continuum (Applied) Numerical Analysis

Spring 2010, Ed Bueler

THANKS for a great semester! 
The projects were excellent, and the take-home exams too.
There were 11 students and 11 pieces of assigned work for each student, and I received 121 to grade!
If you want to see your take-home exam or project then see me.  I need to keep the originals but you can make a copy.



Ed Bueler:  474-7693
elbueler@alaska.edu

Office
: Chapman 301C (Hours)

Class times and rooms:
MWF 1:00--2:00  Chapman 104

Required Text
:  Morton & Mayers, Numerical Solutions of Partial Differential Equations 2nd ed., Cambridge U. Press 2005

Four other texts are recommended.  Two of these are freely available a page at a time:
  • W. Press, et al., Numerical Recipes in C++ (or ... in C or ... in Fortran), Cambridge University Press; any edition.  Pages available free online (using a plugin) at http://www.nrbook.com/a/
  • C. Moler, Numerical Computing with MATLAB, SIAM Press 2004.   ($43 at Amazon.)   Pages and Matlab codes available free online at http://www.mathworks.com/moler/.
  • D. Higham and N. Higham, MATLAB Guide, 2nd ed. SIAM Press 2005.  ($33 at Amazon; other Matlab intros exist, but this one is fun)
  • S. Farlow, Partial Differential Equations for Scientists and Engineers, Dover 1993.  ($11 at Amazon; any PDE book will do and this one may be the cheapest).

Syllabus Here

your Math 615 project


CODES FOR CLASS:


LINKS:

COMMENT on programming languages:  A free alternative to MATLAB is Octave.  It essentially duplicates the functionality of  core MATLAB (but not the MATLAB toolboxes or figure window capabilities).

Another free alternative to MATLAB is the mathematical and scientific support built around the python scripting language, especially the scipy and matplotlib extensions; together they are "pylab".  Generally python allows a programmer to work in the same kind of interpreted prototyping mode as MATLAB/Octave but with much more powerful tools for major projects on supercomputers and clusters, and for systems and internet programming.  (This route is only recommended for more experienced programmers.)
Schedule:  (version 17 May 2010: FINAL)

Day

Section
Topic
Assigned or Due
F 1/22
2.1, 2.2
introduction by example
Assignment #1 (PDF)
M 1/25

cont.
MATLAB/Octave/pylab comparison handout (PDF)

W 1/27

cont.
sewer.m
sewerfcn.m  (slightly improved by making a function)

F 1/29

review of Taylor's theorem and constant coefficient ODEs by-hand; linear ODE example
inclass29jan.m (Matlab-only)
A#1 DUE
M 2/1
2.3 standard heat problem: exact solution by Fourier series/separation of variables
Numerical Analysis by Trefethen (PDF)
A#1 DUE
A#1 Solns (PDF); codes from these solutions at left

Assignment #2 (PDF)
W 2/3
2.4, 2.5
standard heat problem by explicit method:  algorithm and truncation error
F 2/5

cont.

M 2/8

cont.
A#2 DUE
A#2 Solns (PDF); code from these solutions is at left
W 2/10
Bueler away Two-point Boundary Value Problems  (PDF slides)
part I
varheatFD.m
Assignment #3 (PDF; same as last three slides from Two point Boundary Value Problems
F 2/12
Bueler away Two-point Boundary Value Problems  (PDF slides)
part II
varheatSHOOT.m (Octave version)
varheatSHOOTmat.m  (Matlab version)

M 2/15
Bueler away David Maxwell on finite element method I
Assignment #4 =  Maxwell's notes on FEM
(and related Matlab/Octave programs at same link)
W 2/17
Bueler away David Maxwell on finite element method II

F 2/19
Bueler away CLASS CANCELLED

M 2/22
2.6 discussion of A#3 exercises
standard heat problem by explicit method: maximum principle proof of convergence

W 2/24

cont
A#3 DUE
A#3 Solns (PDF); corrected; code from these solutions is at left
F 2/26

discussion of A#4 exercises
refinement paths
refined.m


M 3/1
2.7
standard heat problem by explicit method: fourier analysis of stability Assignment #5 (PDF)
A#4 DUE
W 3/3
2.8, 2.9
standard heat problem by implicit method:  truncation error and implementation
A#4 DUE
A#4 Solns (PDF); code from these solutions is at left
F 3/5
2.12
cont; analysis; also Richardson method
your Math 615 project

3/8-3/12

Spring Break (no classes)

M 3/15
2.10 "theta method" including Crank-Nicolson A#5 DUE
W 3/17

stability for "theta method"
A#5 DUE
A#5 solns distributed in class
F 3/19

cont
Assignment #6 (PDF)
M 3/22
2.13
general boundary conditions
W 3/24
2.14
conservation

F 3/26
2.15
more general linear heat equation (in one spatial dimension)

M 3/29

advection
heatadvect.m
runheatadvect.m
cranknic.m
A#6 DUE AT 5PM
A#6 solns distributed in class
W 3/31

upwinding and divergence form
Assignment #7 (PDF)
F 4/2

cont.
(In class I botched the picture of the stability criterion for explicit upwinded convection-advection.  Here's the scoop:
convect_advect_upwind_stab.m
convect_advect_upwind_stab.pdf   )

PROJECT VERSION 1.0 DUE
M 4/5
2.17 nonlinear diffusivity
W 4/7
6.1
elliptic problems (Poisson equation) in 2 spatial vars by finite difference
fdpoisson.m

F 4/9
3.1
heat equation in 2 spatial vars by explicit
formM.m
A#7 DUE
M 4/12
4.1 pure transport; characteristics A#7 DUE AT 5PM
A#7 solns distributed in class; codes at left
W 4/14
4.2
cont.; connection to classical wave equation; Burger's equation
Assignment #8 (PDF)
F 4/16
4.3
upwinding; CFL; convergence for upwind

M 4/19

cont.

W 4/21
4.5
Lax-Wendroff
upwindfigure.m
lwfigure.m

F 4/23

SpringFest (no classes)
M 4/26
4.9
leapfrog
A#8 DUE AT 5PM ON TUESDAY 4/27
W 4/28
4.4 amplitude and phase errors Assignment #9 (PDF)
F 4/30

cont; recall 6.1

M 5/3
6.2 error analysis for elliptic
W 5/5
6.3 general equilibrium diffusion
for A#8 solns:
upwind.m
lwverify.m
A#8 solns distributed in class
F 5/7
5.1, 5.2 Lax equivalence theorem
OLD NOTES ON DEFINITIONS AND EXAMPLES

W 5/12

A#9 (= TAKE-HOME FINAL EXAM)
IN MY BOX OR OFFICE BY 5:00 PM
some bits of solutions to A#9:
a9prob2a.m
a9prob2b.m
porous.m
leapfigure.m
afpoisson.m
A#9 (= Take-home Final Exam)
DUE AT 5PM

Th 5/13

PROJECT IN MY BOX OR OFFICE BY 5:00 PM PROJECT V2.0
DUE AT 5PM
 
doc info